Write a .Rmd le to answer these questions. Start by pasting this outline to help the grader nd your answers:
(Your Name Here)
• 1 Confidence interval for dissolved oxygen ## 1a
## 1b ## 1c ## 1d
Knit your .Rmd le to .html along the way. Turn in your .html le to Canvas.
1. A simple random sample was taken of 44 water bottles from a bottling plant’s warehouse. The dissolved oxygen content (in mg/L) was measured for each bottle, with these results:
11.53, 8.35, 11.66, 11.54, 9.83, 5.92, 7.14, 8.41, 8.99, 13.81, 10.53, 7.4, 6.7, 8.42, 8.4, 8.18, 9.5, 7.22, 9.87, 6.52, 8.55, 9.75, 9.27, 10.61, 8.89, 10.01, 11.17, 7.62, 6.43, 9.09, 8.53, 7.91, 8.13, 7.7, 10.45, 11.3, 10.98, 8.14, 11.48, 8.44, 12.52, 10.12, 8.09, 7.34
Here the sample mean is 9.14 mg/L.
The population standard deviation of the dissolved oxygen content for the warehouse is known from long experience to be about = 2 mg/L.
(a) Find a 98% con dence interval for the unknown population mean dissolved oxygen content.
(b) Interpret your interval|in particular, what does the \98% con dence" mean?
(c) What sample size n is required to get a 98% con dence interval with error margin 0.5?
(d) To make a Z con dence interval, we must assume that the sample mean is (approximately) normally distributed, which it will be if the population is normal or the sample size is large enough{that is, if n > 30 by our rule-of-thumb.
Here we have n = 44, so we do not need to check for a normal population. However, as practice for when n is smaller, make a normal QQ-plot of the sample. Is it plausible that the sample came from a normal population?
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